You have a good point. This question is a little ambiguous. However, simply taking the union of two sets means that the resulting function f+g is multivalued at -4, for example, which means it's no longer a function.
Adding the outputs of the two functions is also a little tricky, since f is defined at 3, for example, while g is not. The sum of the two functions at 3 is thus also undefined, since anything + undefined = undefined.
The first set is f(x), for x values -4, -2, 1, 3, and 4.
The second set is g(x), for x values -4, -2, 0, 1, 2, and 4.
The only input values common to both functions are -4, -2, 1, and 4. These are thus the input values acceptable to the function f+g. All other possible input values have no defined output.
The output values of f+g are each the sum of the outputs of f and g at the same point. Thus, if you plug in -4 to f+g, you get f(-4) + g(-4) = 4+2 = 6.